Details

analyze3.0s (15.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

Compiler

Compiled 20 to 18 computations (10% saved)

sample268.0ms (1.4%)

Algorithm

1×

intervals

Results

186.0ms	179×	body	1024	valid
35.0ms	14×	body	2048	valid
23.0ms	40×	body	512	valid
6.0ms	18×	body	256	valid
1.0ms	5×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify182.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	78	31
1	78	31

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 14.2b

Counts

2 → 1

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
0.7b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
1.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite23.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_100`
9×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
8×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `pow1_binary64_139`
6×	`associate-l_binary64_19` `associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `cos-sum_binary64_212`
3×	`cancel-sign-sub-inv_binary64_44`
2×	`*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46`
1×	`acos-asin_binary64_259` `sin-mult_binary64_233` `cos-diff_binary64_215` `sub-neg_binary64_71`

Counts

4 → 57

Calls

4 calls:

6.0ms	(cos.f64 (-.f64 lambda1 lambda2))
6.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

series395.0ms (2%)

Counts

4 → 12

Calls

4 calls:

227.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
72.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
63.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
33.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify76.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4863	1492
1	4863	1492

prune107.0ms (0.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	53	16	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	16	70

Merged error: 3.7b

Counts

70 → 16

Compiler

Compiled 2210 to 588 computations (73.4% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.2b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.7b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64_114` `add-sqr-sqrt_binary64_100` `add-exp-log_binary64_116` `pow1_binary64_139`
9×	`add-cube-cbrt_binary64_113` `associate-r_binary64_18` `*-un-lft-identity_binary64_78`
7×	`associate-l_binary64_19`
6×	`cos-mult_binary64_232`
5×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149`
4×	`add-log-exp_binary64_117`
3×	`-commutative_binary64_9` `frac-times_binary64_88` `sin-mult_binary64_233` `associate-r/_binary64_20`
2×	`frac-add_binary64_86` `flip-+_binary64_52` `unswap-sqr_binary64_46` `flip3-+_binary64_81`
1×	`distribute-lft-in_binary64_27` `distribute-rgt-in_binary64_28` `acos-asin_binary64_259` `associate-*l/_binary64_21`

Counts

4 → 72

Calls

4 calls:

12.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series932.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

422.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
335.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
103.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
72.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

simplify81.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5063	2773

prune141.0ms (0.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	70	14	84
Fresh	11	4	15
Picked	1	0	1
Done	0	0	0
Total	82	18	100

Merged error: 3.5b

Counts

100 → 18

Compiler

Compiled 3633 to 786 computations (78.4% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.4b	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
0.4b	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
0.7b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_100`
9×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
7×	`pow1_binary64_139`
6×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `exp-prod_binary64_130`
5×	`add-log-exp_binary64_117`
4×	`log-pow_binary64_167`
3×	`associate-l_binary64_19` `acos-asin_binary64_259` `associate-r_binary64_18` `log-prod_binary64_164`
2×	`exp-diff_binary64_126`
1×	`*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `rem-exp-log_binary64_118` `rem-log-exp_binary64_119` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `log-div_binary64_165` `sin-mult_binary64_233`

Counts

4 → 55

Calls

4 calls:

6.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
3.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
2.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series698.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

344.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
198.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
86.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
69.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

simplify100.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4864	2288
1	4864	2288

prune128.0ms (0.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	60	7	67
Fresh	4	13	17
Picked	1	0	1
Done	0	0	0
Total	65	20	85

Merged error: 3.5b

Counts

85 → 20

Compiler

Compiled 3375 to 780 computations (76.9% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.6b	(cbrt.f64 (pow.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) 3))
0.7b	(pow.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) 3)
0.7b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) 3))))

rewrite41.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`cube-div_binary64_107`
12×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `cos-mult_binary64_232` `pow1_binary64_139`
10×	`add-sqr-sqrt_binary64_100`
8×	`add-cube-cbrt_binary64_113` `cbrt-prod_binary64_109` `*-un-lft-identity_binary64_78`
7×	`cbrt-div_binary64_110`
6×	`frac-times_binary64_88` `associate-*r/_binary64_20`
5×	`sin-mult_binary64_233`
4×	`frac-add_binary64_86` `add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `pow-prod-down_binary64_149` `flip3-+_binary64_81`
3×	`rem-cube-cbrt_binary64_101` `associate-l_binary64_19` `pow-exp_binary64_146` `associate-r_binary64_18` `pow-pow_binary64_150` `pow-unpow_binary64_155`
2×	`cube-mult_binary64_108` `unpow-prod-down_binary64_157` `sqr-pow_binary64_50` `associate-*l/_binary64_21` `unpow3_binary64_144` `cube-prod_binary64_106`
1×	`*-commutative_binary64_9` `rem-cbrt-cube_binary64_102` `pow-to-exp_binary64_147` `pow1/3_binary64_160` `acos-asin_binary64_259` `unswap-sqr_binary64_46`

Counts

4 → 83

Calls

4 calls:

13.0ms	(pow.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) 3)
8.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) 3))
6.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) 3))))

series1.5s (7.8%)

Counts

4 → 12

Calls

4 calls:

950.0ms	(pow.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) 3)
410.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) 3))
97.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) 3))))
65.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

simplify72.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5334	3099

prune122.0ms (0.6%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	19	19
Picked	0	1	1
Done	0	0	0
Total	95	20	115

Merged error: 3.5b

Counts

115 → 20

Compiler

Compiled 3575 to 716 computations (80% saved)

regimes1.8s (9.1%)

Compiler: Compiled 26064 to 15664 computations (39.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	43
1	31	43

end0.0ms (0%)

sample9.7s (49.5%)

Algorithm

1×

intervals

Results

5.7s	5489×	body	1024	valid
868.0ms	1444×	body	512	valid
653.0ms	259×	body	2048	valid
198.0ms	508×	body	256	valid
57.0ms	300×	body	128	valid
5.0ms	5×	body	1024	invalid

Compiler

Compiled 2484 to 1490 computations (40% saved)

Details

analyze3.0s (15.5%)

sample268.0ms (1.4%)

simplify182.0ms (0.9%)

prune4.0ms (0%)

localize25.0ms (0.1%)

rewrite23.0ms (0.1%)

series395.0ms (2%)

simplify76.0ms (0.4%)

prune107.0ms (0.5%)

localize33.0ms (0.2%)

rewrite33.0ms (0.2%)

series932.0ms (4.7%)

simplify81.0ms (0.4%)

prune141.0ms (0.7%)

localize37.0ms (0.2%)

rewrite20.0ms (0.1%)

series698.0ms (3.6%)

simplify100.0ms (0.5%)

prune128.0ms (0.7%)

localize36.0ms (0.2%)

rewrite41.0ms (0.2%)

series1.5s (7.8%)

simplify72.0ms (0.4%)

prune122.0ms (0.6%)

regimes1.8s (9.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample9.7s (49.5%)

Profiling